Aptitude question and answer for Bank preparation

1. OBJECTIVE-TYPE QUESTIONS
253 s OCTOBER 2001 s THE COMPETITION MASTER
Quantitative Aptitude
1. A square garden has fourteen posts along each side
at equal interval. Find how many posts are there in all four
sides:
(a) 56 (b) 52 (c) 44 (d) 60
2. Average age of students of an adult school is 40 years.
120 new students whose average age is 32 years joined the
school. As a result the average age is decreased by 4 years.
Find the number of students of the school after joining of the
new students:
(a) 1200 (b) 120 (c) 360 (d) 240
3. When Rs 250 added to 1/4th of a given amount of
money makes it smaller than 1/3rd of the given amount of
money by Rs 100. What is the given amount of money?
(a) Rs 350 (b) Rs 600 (c) Rs 4200 (d) Rs 3600
4. Find the least number of candidates in an examination
so that the percentage of successful candidates should be
76.8%:
(a) 500 (b) 250 (c) 125 (d) 1000
5. The number of times a bucket of capacity 4 litres to
be used to fill up a tank is less than the number of times
another bucket of capacity 3 litres used for the same purpose
by 4. What is the capacity of the tank?
(a) 360 litres (b) 256 litres (c) 48 litres (d) 525 litres
6. Simplify:
1
1
1
1
1
1
1
2
+
+
+
(a)
8
5
(b)
5
8
(c)
1
2
(d)
3
2
7. Acertain quantity of rice is spent daily for 30 students
in a hostel. One day some students were absent as a result, the
quantity of rice has been spent in the ratio of 6 : 5. How many
students were present on that day?
(a) 24 (b) 20 (c) 15 (d) 25
8. The ratio of daily wages of two workers is 4 : 3 and
one gets daily Rs 9 more than the other, what are their daily
wages?
(a) Rs 32 and Rs 24 (b) Rs 60 and Rs 45
(c) Rs 80 and Rs 60 (d) Rs 36 and Rs 27
9. Find the ratio of purchase price and sell price if there
is loss of 12
1
2
%.
(a) 7 : 8 (b) 8 : 7 (c) 2 : 25 (d) 25 : 2
10. The simplified value of 1.2 + (1.2)2
+ (1.2)3
is:
(a) 4.248 (b) 4.368 (c) 3.248 (d) 3.368
11. The rate of failure in an examination is 39.25%. Find
the least number of total candidates appeared in the
examination.
(a) 500 (b) 400 (c) 125 (d) 260
12. Find H.C.F. of
3
5
, .36, .24
(a) .04 (b) 2
(c) .4 (d) None of the above
13. 0.8 portion of a tank is filled with water. If 25 litres of
water is taken out from the tank, 14 litres of excess water over
the half filled up tank remains in it. Find the capacity of the
tank.
(a) 100 litres (b) 130 litres
(c) 200 litres (d) 150 litres
14. The ratio of ages of two persons is 4 : 7 and one is 30
years older than the other. Find the sum of their ages.
(a) 210 years (b) 110 years (c) 90 years (d) 140 years
15. The ratio of the age of a gentleman and his wife is
4 : 3. After 4 years this ratio will be 9 : 7. If at the time of their
marriage the ratio was 5 : 3, how many years ago they were
married?
(a) 10 years (b) 8 years
(c) 12 years (d) 15 years
16. Simplify:
1 3 1 3 1 3 1
1 3 1 3 1 3 1
. . .
. . .
. . .
. . .
× × −
× + +
(a) .3 (b) 3
1
3
(c) .
.
3 (d) 1
17. What sum of money is to be divided among 3 men in
the ratio 3 : 4 : 5 so that the third man receives Rs 10 only.
(a) Rs 56 (b) Rs 84 (c) Rs 120 (d) Rs 24
18. Sum of two numbers prime to each other is 20 and
their L.C.M. is 99. What are the numbers?
(a) 8 and 12 (b) 14 and 6
(c) 19 and 1 (d) 11 and 9
19. Find square root of 2 7.
.
(a) .5 (b) 5 (c) 1
2
3
(d) .3
20. Find the greatest of the four least common multiples
of 3, 5 and 7.
(a) 1 (b) 420 (c) 315 (d) 105
Solved Paper of Cooperative Bank Exam, 2000

2. OBJECTIVE-TYPE QUESTIONS
254 s OCTOBER 2001 s THE COMPETITION MASTER
21. Find the greatest number which on dividing 107 and
120 leaves remainders 5 and 1 respectively.
(a) 25 (b) 6 (c) 9 (d) 17
22. Express Rs 25 as percentage of Rs 75:
(a) 3% (b) 30% (c) .
.
3% (d) 33 3. %
.
23. 25% of X = 45% of Y. Then X : Y is:
(a) 5 : 9 (b) 3 : 5 (c) 5 : 3 (d) 9 : 5
24. The value of 99
1
7
99
2
7
99
3
7
99
4
7
99
5
7
99
6
7
+ + + + + is:
(a) 594 (b) 595 (c) 596 (d) 597
25. If n is any positive odd integer greater than 1, the
n(n2
– 1) is always divisible by:
(a) 7 (b) 5 (c) 24 (d) 15
26. The value of {(.87)3
+ (.13)3
+ .87 × .39}0.5
is:
(a) 0.6 (b) 1 (c) 0 (d) 3
27. A hawker purchased oranges at the rate of 4 oranges
in a rupee, but he sells at the rate of 5 oranges in a rupee. His
loss is:
(a) 20% (b) 25% (c) 50% (d) 100%
28. A businessman purchased 35 kg dal of Rs 525 and
sells it at the rate of Rs 18 per kg. Then the rate of profit or loss
is:
(a) 20% profit (b) 25% loss (c) 25% profit (d) 20% loss
29. The difference and the product of two numbers are
32 and 2145 respectively. Their sum is:
(a) 89 (b) 98 (c) 78 (d) 87
30. The sum of two numbers is 45 and their product is
500. The G.C.M. of the numbers is:
(a) 5 (b) 9 (c) 10 (d) 15
31. The simplest value of
5 2
5 2
5 2
5 2
+
−
+
−
+
:
(a) 9 (b) 1 (c) 14 (d) 18
32. The sum of the present age of the father and his
daughter is 42 years. 7 years later, the father will be 3 times
old than the daughter. The present age of the father is:
(a) 35 (b) 28 (c) 32 (d) 33
33. If x < 5, which one is true?
(a) x3
> 125 (b) x3
< 125 (c) x3
≥ 125 (d) x3
≤ 125
34. The average of the first four of five numbers is 40 and
that of the last four numbers is 60. The difference of the last
and the first number is:
(a) 400 (b) 200 (c) 40 (d) 80
35. The numbers which divide 80 in such a way that the
sum of their reciprocals is
4
75
are:
(a) 40, 40 (b) 35, 45 (c) 30, 50 (d) 60, 20
36. 20 labourers can do a work in 20 days if everybody
works for 6 hours daily. Then 25 labourers can do the same
work in 12 days by working daily for:
(a) 8 hours (b) 6 hours (c) 4 hours (d) 10 hours
37. The value of 3 3. %
.
of Rs 300 is:
(a) Rs 9.90 (b) Rs 11
(c) Rs 10 (d) None of the above
38. Two identical bottles Aand B of sweet drinks contain
sugar such that 30% of sugar in A is equal to 40% sugar in B.
The ratio of sugar in the two bottles is:
(a) 4 : 3 (b) 3 : 4 (c) 12 : 1 (d) 1 : 12
39. The volume is decreased by 10% when ice is melted
into water. If water is freezed, the volume is increased by:
(a) 11
1
10
% (b) 11
1
9
% (c) 9
1
11
% (d) 10%
40. The greatest two digit number whose square root is
an integer is:
(a) 99 (b) 89 (c) 81 (d) 10
41. If A : B = 3 : 4, C : B = 5 : 4, C : D = 10 : 9, then
A : B : C : D is:
(a) 6 : 8 : 10 : 9 (b) 8 : 6 : 9 : 10
(c) 8 : 6 : 10 : 9 (d) 6 : 8 : 9 : 10
42. If 20% of A = 30% of B =
1
6
th of C, then A : B : C is:
(a) 2 : 3 : 16 (b) 3 : 2 : 16
(c) 10 : 15 : 18 (d) 15 : 10 : 18
43. If A = 2 +
1
a
and B = a +
1
2
then A = B if a is:
(a)
1
2
(b) –
1
2
(c) 2 (d) – 2
44. A man retired from his service at the age of 60. He
served for
3
5
th years of his retirement age. He joined his job
at the age of:
(a) 36 years (b) 24 years (c) 18 years (d) 30 years
45. If
a
2
b
7
c
5
= = , then the value of
a b c
a b c
− +
+ −
is:
(a) 0 (b) 1 (c) 3 (d) ∝
46. The least number divisible by any integer between 1
and 9 is:
(a) 2250 (b) 5220 (c) 2520 (d) 2025
47. The value of
. . . . . .
. . . . . .
7 7 7 6 6 6
7 7 6 6 7 6
× × − × ×
× + × + × is:
(a) 0.1 (b) 1 (c) 1.3 (d) 1.1
48. A number is increased consecutively two times by
20% each. The original number is actually increased by:
(a) 40% (b) 42% (c) 44% (d) 20%
49. 42 oranges are distributed among some boys and girls.
If each boy gets 3 then each girl gets 6. But if each boy gets 6
and each girl gets 3, it needs 6 more. The number of girls is:
(a) 4 (b) 6 (c) 8 (d) 10
50. An alloy of zinc and copper contains the metals in
the ratio 5 : 3. The quantity of zinc to be added to 16 kg of the
alloy so that the ratio of the metal may be 3 : 1 is:
(a) 2 kg (b) 4 kg (c) 3 kg (d) 8 kg

3. OBJECTIVE-TYPE QUESTIONS
255 s OCTOBER 2001 s THE COMPETITION MASTER
1. (b) Reqd no. of posts = 4 (at the corners) + 4 × 12
(in between on the sides)
= 4 + 48 = 52
2. (d) Let the original no. of students be x
A.T.S. 40x + 120 × 32 = (x + 120)36 ⇒ x = 120
∴ Reqd no. of students after joining the new students
= x + 120 = 240
3. (c) Let the given amount be Rs x
A.T.S.
x
3
(
x
4
250) 100− + = ⇒ x = Rs 4200
4. (c) No. of successful candidates = 76.8% of x
x = total students
=
×
× =(
768
10 100
x)
96
125
x
Which must be a whole no. ∴The reqd least no. = 125
5. (c)
x
4
x
3
x 48− = ⇒ =4 l
1
1
1
1
1
3
2
1
1
1
1
2
3
+
+
=
+
+
=
+
1
1
1
5
3
=
+
= =
1
1
3
5
1
8
5
5
8
7. (d) Reqd no. of students = 30 ×
5
6
= 25 [ ]Q
30
x
=
6
5
8. (d)
x 9
x
+
= ⇒
4
3
x = 27
Their daily wages are Rs 27 + 9, Rs 27 i.e. Rs 36, Rs 27
9. (b) Reqd ratio = =
−
=
C.P.
S.P.
100
100
25
2
8
7
S.P.=C.P.–Loss
= 8 : 7
10. (b) 1.2 + 1.44 + 1.728 = 4.368
11. (b) No. of failures = 39.25% of x =
×
×
3925
100 100
x
=
157
400
x which must be a whole no.
∴ x = 400 (least no.)
12. (d) H.C.F. of
3
5
36
100
24
100
, , =
HCFof 3, 9, 6
LCMof 5,25,25
=
3
25
= .12
13. (b) .8 =
4
5
A.T.S.
4
5
x – 25 =
x
2
+ 14 ⇒ x = 130
14. (b)
x
x 30
x
+
= ⇒ =
4
7
40 Sum of ages = x + x + 30 = 110
or 7x – 4x = 30 ⇒ x = 10 ∴ Sum of ages = 11x = 110
15. (c)
4x 4
3x 4
x
+
+
= ⇒ =
9
7
8
Man’s present age = 32 years, woman’s age = 24 yrs
Let the reqd time be y years
∴
32 5
3
−
−
= ⇒ =
y
24 y
y 12years
16. (c)
a b
a ab b
a b
3 3
2 2
−
+ +
= ,
( . )
( . ) . ( )
. .
.
. .
. .1 3 1
1 3 3 1 1
1 3 1 3
3 3
2 2
−
+ × +
= − =
17. (d)
5
3 4 5
10 24
+ +
× = ⇒ =x x Rs
18. (d)
19. (c) 2 7 2 7 2
7
9
25
9
. . ,
. .
= + = + = 2 7.
.
=
25
9
=
5
3
= 1
2
3
20. (b) L.C.M. of 3, 5, 7 = 105
Four least common multiples of 3, 5, 7 are 105, 210,
315, 420 ∴ Greatest = 420
21. (d) 107 120
– 5 – 1
102 119 Reqd no. = HCF of 102 and 119 = 17
22. (d) x% of 75 = 25 ⇒ x =
25
75
100 33 3× = .
23. (d)
25
100
45
100
45
25
× = ⇒ =X Y
X
Y
= ⇒
9
5
X : Y = 9 : 5
24. (d) Value = 99 × 6 +
1
7
2
7
3
7
4
7
5
7
6
7
+ + + + +
= 594 +
21
7
594 3 597= + =
25. (c) n(n2
– 1) = n(n – 1) (n + 1) Take n = 3 (Q n ≥ 1)
= 3 × 2 × 4 = 24 (Always take least no.)
Which is divisible by 24
26. (b) (.87)3
+ (.13)3
+ 3 × .87 × .13 (.87 + .13) = (.87 + .13)3
= (1.00)3
= 1 (.87 + .13 = 1.00)
a3
+ b3
+ 3ab (a + b) = (a + b)3
27. (a) Let the no. of oranges be 20 (L.C.M. of 4 & 5)
C.P. =
1
4
20 5× = Rs , S.P. =
1
5
20 4× = Rs
∴ Loss = 5 – 4 = Re 1
Loss% =
Loss
C.P.
100
1
5
100 20× = × =
28. (a) C.P. of 1 kg dal =
525
35
= Rs 15, S.P. = Rs 18
Profit = S.P. – C.P. = 18 – 15 = Rs 3, P% =
3
15
100 20× =
ANSWERS AND EXPLANATIONS
6. (b)

4. OBJECTIVE-TYPE QUESTIONS
256 s OCTOBER 2001 s THE COMPETITION MASTER
29. (b) x – y = 32 ∴ x = 32 + y
Product = y(32 + y) = 2145
or y2
+ 32y – 2145 = 0 ⇒ y2
+ 65y – 33y – 2145 = 0
y(y + 65) – 33 (y + 65) = 0 ⇒ (y – 33) (y + 65) = 0
⇒ y = 33, –65 y ≠ 65 ∴ y = 33
The sum of nos. = y + (y + 32) = 2y + 32
= 2 × 33 + 32 = 98
30. (a) Let the nos. be x, 45 – x A.T.S x(45 – x) = 500
x2
– 45x + 500 = 0 ⇒ x2
– 20x – 25x + 500 = 0
x(x– 20) – 25 (x – 20) = 0 ⇒ (x – 20) (x – 25) = 0
x = 25, 20. If one no. = 25 other no. = 45 – 25 = 20
G.C.M. of 25, 20 = 5
31. (d) Value =
+ + −
−
( ) ( )
( )
5 2 5 2
5 2
2 2
2 2
=
+ + + + −
−
5 4 4 5 5 4 4 5
5 4
= 18
32. (a) Let father’s present age be x years
∴ Son’s present age 42 – x years
A.T.S x + 7 = 3(42 – x + 7) ⇒ x = 35 years
33. (b)
34. (d) x1
+ x2
+ x3
+ x4
= 4 × 40 = 160
x2
+ x3
+ x4
+ x5
= 4 × 60 = 240
Subtracting x1
– x5
= – 80 or x5
– x1
= 80
35. (c)
36. (a) Men Days Hours
20 20 6
25 12 x
More men less hours
25 : 20
Less days more hours
12 : 20
∴
× ×
×
=x =
6 20 20
25 12
8
37. (c) 3 3 3
3
9
10
3
.
.
= + =
3 3.
.
% of Rs 300 =
10
3 100
300
×
× = Rs 10
38. (a) 30% of x = 40% of y ⇒
30
100
x =
40
100
y ⇒
x
y
=
4
3
= 4 : 3
39. (b) Volume of ice = x (say)
∴ Volume of water (when ice melted)
=
(100 10)
100
x =
9
10
x
When water is freezed, it changes into ice
Volume becomes = x
∴ Increase = x
9x
10
=
x
10
If vol. of water =
9x
10
, increase in vol. (when freezed)
=
x
10
If volume of water 100, increase in volume
=
x
10 x
× × =
10
9
100 11
1
9
%
40. (c) 81 9=
41. (a) A : B : C A : B : C : D
3 : 4 12 : 16 : 20
4 : 5 10 : 9
12 : 16 : 20 120 : 160 : 200 : 180 or 6 : 8 : 10 : 9
42. (d)
20
100
A =
30
100
B =
C
6
or
A
5
=
B
10
3
=
C
6
∴ A : B : C = 5
10
3
6: : or 15 : 10 : 18
43. (b & c) A = B ⇒ 2+
1
a
= a +
1
2
⇒ 2a2
– 3a – 2 = 0
⇒ (2a + 1) (a – 2) = 0 ⇒ a = 2, –
1
2
44. (b) He served for 60 ×
3
5
= 36 years
∴ He joined his job at the age of 60 – 36 = 24 years
45. (a)
a
2
b
7
c
5
= = = k, a = 2k, b = 7k, c = 5k
a b c
a b c
− +
+ −
=
2k 7k 5k
2k 7k 5k
− +
+ −
=
0
4k
= 0
46. (c)
47. (a)
a b
a b ab
3 3
2 2
−
+ +
= a – b = .7 – .6 = 0.1
48. (c) Let the no. be 100
No. after increasing consecutively two times
= 100
120
100
120
100
144× × =
∴ The original no. is actually increased by
144 – 100 = 44 44%
49. (a) Let the no. of boys be x and that of girls be y
A.T.S. 3x + 6y = 42 or x + 2y = 14 ... (i)
6x + 3y = 42 + 6 ⇒ 2x + y = 16 ... (ii)
Solving (i) and (ii) we get y = 4
50. (d) Zinc =
5
8
16 10× = kg Copper = 6 kg
A.T.S.
10
6
3
1
+
= ⇒
x
x = 8 kg
: : 6 : x
}